Road friction coefficients estimating apparatus for vehicle

ABSTRACT

A road friction coefficient estimating apparatus for a vehicle includes a high friction coefficient road reference value estimating section for calculating a high friction coefficient road reference yaw rate based on a vehicle motion model when the vehicle travels on a road surface with high friction coefficient, an actual value estimating section for calculating an actual yaw rate, a Lissajou figure processing section for forming a Lissajou&#39;s figure based on the high friction coefficient road reference yaw rate and the actual yaw rate and for calculating a gradient and area of this Lissajou&#39;s figure, a road friction coefficient estimating section for estimating a road friction coefficient based on the area of the Lissajou&#39;s figure when the gradient is in the neighborhood of 45 degrees and for estimating a road friction coefficient based on a lateral acceleration when the gradient is out of the neighborhood of 45 degrees.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention relates to a road friction coefficientsestimating apparatus for a vehicle for estimating friction coefficientson road surfaces and more particularly to a road friction coefficientsestimating apparatus capable of accurately estimating frictioncoefficients on road surfaces by a simple method using vehicle motionparameters such as lateral acceleration, yaw rate and the like.

[0003] 2. Discussion of Prior Arts

[0004] In recent years, numerous vehicle control technologies such astraction control technologies, braking force control technologies,torque distribution control technologies and the like, have beenproposed and some of these control technologies have been realized inactual automobile markets. Many of these control technologies usefriction coefficients on road surfaces (hereinafter, referred to as“road friction coefficient”) for calculation or correction of controlparameters. Accordingly, in order to execute the control properly, it isnecessary to estimate accurate road friction coefficients.

[0005] Several technologies in which road friction coefficients areestimated based on vehicle motion parameters such as lateralacceleration, yaw rate have been proposed. For example, the applicant ofthe present invention proposes a technology in which road frictioncoefficients are estimated based on the comparison of an actual yaw rateestimated from an observer with a yaw rate calculated using a vehiclemotion model on a high friction coefficient road surface and a yaw ratecalculated using a vehicle motion model on a low friction coefficientroad surface respectively in Japanese Patent Application No.Toku-Gan-Hei 11-217508.

[0006] However, since the above technology needs two vehicle motionmodels, high and low friction coefficient road surface models, thetechnology has a disadvantage of taking much time for tuning.Particularly, in case of the low friction coefficient road surfacemodel, it is necessary to take a nonlinearity of tire into considerationand therefore the vehicle motion model becomes complicated and this is aprimary cause of taking much time for tuning. Further, since the abovetechnology is constituted by two vehicle motion models, the technologyhas a defect of complicated logic and large amount of calculations.

SUMMARY OF THE INVENTION

[0007] It is an object of the present invention to provide a vehicularroad friction coefficient estimating apparatus having a simpleconstruction and a small amount of calculations and capable of easilymaking a tuning and stably and accurately estimating road frictioncoefficients over broad traveling conditions.

[0008] The road friction coefficient estimating apparatus for a vehiclecomprises an actual value estimating means for estimating an actualvalue of a vehicle motion parameter, a high friction coefficient roadreference value estimating means for estimating a high frictioncoefficient road reference value of the vehicle motion parameter basedon a vehicle motion model when the vehicle travels on a road surfacewith high friction coefficient and a road friction coefficientestimating means for forming a Lissajou's figure based on the actualvalue and the high friction coefficient road reference value and forestimating a road friction coefficient according to an area of theLissajou's figure when a gradient of the Lissajou's figure is in theneighborhood of 45 degrees and for estimating a road frictioncoefficient according to a lateral acceleration of the vehicle when thegradient is in a range out of the neighborhood of 45 degrees.

DESCRIPTION OF THE DRAWINGS

[0009]FIG. 1 is a functional block diagram showing a road frictioncoefficient estimating apparatus according to an embodiment of thepresent invention;

[0010]FIG. 2 is a diagram showing a two wheel vehicle model equivalentto a four wheel vehicle;

[0011]FIG. 3 is a circuit diagram showing a basic construction of anobserver;

[0012]FIG. 4 is an explanatory view showing an integrating range;

[0013]FIG. 5 is an explanatory view showing a calculation of an area ofLissajou's figure;

[0014]FIG. 6 is an explanatory view of a steering pattern variable;

[0015]FIG. 7 is an explanatory view of a method of calculating a roadfriction coefficient estimating value μ_(A);

[0016]FIGS. 8a to 8 c are explanatory views showing various Lissajou'sfigures drawn by two waveforms;

[0017]FIG. 9a is an explanatory view showing an effect of nonlinearityof tire;

[0018]FIG. 9b is an explanatory view showing an effect of nonlinearityof tire; and

[0019]FIG. 10 is a flowchart showing steps for calculating a roadfriction coefficient estimating value according to an embodiment of thepresent invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

[0020] Referring now to FIG. 1, reference numeral 1 denotes a roadfriction coefficient estimating apparatus mounted on a vehicle forestimating road friction coefficients and reference numeral 2 denotes acontrol section of the road friction coefficient estimating apparatus 1.The control section 2 is connected with a front wheel steering anglesensor 3, a vehicle speed sensor 4, a lateral acceleration sensor 5 anda yaw rate sensor 6 and inputs signals of front wheel steering anglesδ_(fs), vehicle speed V_(s), lateral acceleration (d²y/dt²)_(s), yawrate (dφ/dt), (yaw angular velocity) from respective sensors. Asubscript “_(s)” is for indicating a value arisen from a sensor.

[0021] The control section 2 estimates and outputs road frictioncoefficients. The control section 2 comprises a high frictioncoefficient road reference value estimating section 11, an actual valueestimating section 12, a Lissajou figure processing section 13 and aroad friction coefficient estimating section 14.

[0022] The high friction coefficient road reference value estimatingsection 11 inputs vehicle speed V_(s) and front wheel steering angleδ_(fs), calculates high friction coefficient road reference yaw rate(dφ/dt)_(H) corresponding to the detected vehicle speed V_(s) and frontwheel steering angle δ_(fs) according to a vehicle motion model on thebasis of an equation of vehicle motion on a road surface with highfriction coefficient and outputs the high friction coefficient roadreference yaw rate (dφ/dt)_(H) to the Lissajou figure processing section13. Further, the high friction coefficient road reference valueestimating section 11 outputs yaw rate (d²φ/dt²)_(s) besides the highfriction coefficient road reference yaw rate (dφ/dt)_(H) to the Lissajoufigure processing section 13. The subscript “_(H)” of parametersoutputted from the high friction coefficient road reference valueestimating section 11 denotes high friction coefficient road referencerelated parameters.

[0023] A vehicle motion model used in the high friction coefficient roadreference value estimating section 11 and the calculation of parameterswill be described by reference to FIG. 2. The equation of lateraltransitional motion of a vehicle is expressed using the vehicle motionmodel illustrated in FIG. 2 as:

M·(d ² y/dt ²)=2·F _(f)+2·F _(r)   (1)

[0024] where M is mass of a vehicle; F_(f), F_(r) are cornering forcesof front and rear wheels, respectively; and d²y/dt² is lateralacceleration.

[0025] On the other hand, the equation of rotational motion aroundgravity center of the vehicle is expressed as:

I _(z)·(d ² φ/dt ²)=2·F _(f) ·L _(f)−2·F _(r) ·L _(r)   (2)

[0026] where I_(z) is yaw moment of inertia of the vehicle; L_(f), L_(r)are distances from the center of gravity to the front and rear wheels,respectively; and (d²φ/dt²) is yaw angular acceleration.

[0027] Further, the lateral acceleration (d²y/dt²) is expressed as:

(d ² y/dt ²)=V·((dβ/dt)+(dφ/dt)   (3)

[0028] where V is vehicle speed; β is slip angle of a vehicle; and(dβ/dt) is slip angular velocity of a vehicle.

[0029] The cornering forces have a response similar to a first-ordertime lag. In this case, this time lag being neglected and letting thecornering forces be linearized introducing an idea of equivalentcornering power in which suspension characteristic is involved in tirecharacteristic, the cornering forces are expressed as follows:

F _(f) =−K _(f)·β_(f)   (4)

F _(r) =−K _(r)·β_(r)   (5)

[0030] where K_(f), K_(r) are equivalent cornering powers of front andrear wheels, respectively; and β_(f), β_(f) are lateral slip angles offront and rear wheels, respectively.

[0031] Using equivalent cornering powers and taking the effect of rolland suspension of the vehicle into consideration, lateral slip anglesβ_(f), β_(r) are can be simplified as follows:

β_(f) =β+L _(f)·(dφ/dt)/V−δ _(f)   (6)

β_(r) =β−L _(r)·(dφ/dt)/V   (7)

[0032] where δ_(f) is steering angle of front wheel.

[0033] The following equation of state is obtained from the aforesaidequations of motion:

(dx(t)/dt)=A·x(t)+B·u(t)   (8)

x(t)=[β(dφ/dt)]^(T)

u(t)=[δ_(f)0]^(T)

[0034] $A = \begin{bmatrix}a_{11} & a_{12} \\a_{21} & a_{22}\end{bmatrix}$ $B = \begin{bmatrix}b_{11} & b_{12} \\b_{21} & b_{22}\end{bmatrix}$

a ₁₁=−2·(K _(f) +K _(r))/(M·V)

a ₁₂=−1−2·(L _(f) ·K _(f) −L _(r) ·K _(r))/(M·V ²)

a ₂₁=−2·(L _(f) ·K _(f) −L _(r) ·K _(r))/I _(z)

a ₂₂=−2·(L _(f) ² ·K _(f) +L _(r) ² ·K _(r))/(I _(z) ·V)

b ₁₁=2·K _(f)/(M·V)

b ₂₁=2·L _(f) ·K _(f) /I _(z)

b ₁₂ =b ₂₂=0

[0035] In the high friction coefficient road reference value estimatingsection 11, a high friction coefficient road reference based slipangular velocity (dβ/dt)_(H) and a refernce road based yaw angularacceleration (d²φ/dt²)_(H) are obtained by calculating(dx(t)/dt)=[(dβ/dt) (d²φ/dt²)]^(T) in a vehicle operating condition(vehicle speed V, front wheel steering angle δ_(f)), when equivalentcornering powers K_(f), K_(r) at 1.0 for example of road frictioncoefficient have been established beforehand in the formula (8). Then, ahigh friction coefficient road reference vehicle slip angle β_(H) and ahigh friction coefficient road reference yaw rate (dφ/dt)_(H) areobtained by integrating the vehicle slip angular velocity (dβ/dt)_(H)and the yaw angular acceleration (d²φ/dt²)_(H).

[0036] The actual value estimating section 12 inputs vehicle speedV_(s), front wheel steering angled δ_(fs), lateral acceleration(d²y/dt²)_(s) and yaw rate (dφ/dt)_(s) and calculates an actual yaw rate(dφ/dt)₀ while actual vehicle behaviors are fed back. That is, theactual value estimating section 12 is an observer derived from thevehicle motion model. The actual yaw rate (dφ/dt)₀ calculated in theactual value estimating section 12 is outputted to the Lissajou's figureprocessing section 13. The subscript “0” attached to the actual yaw rate(dφ/dt)₀ denotes a parameter originated from the observer.

[0037] The construction of the observer according to this embodimentwill be described by reference to FIG. 3.

[0038] When the output detected by the sensor is expressed as follows:

y(t)=C·x(t)   (9)

[0039] The construction of the observer is:

(dx′(t)/dt)=(A−K·C)·x′(t)+K·y(t)+B·u(t)  (10)

[0040] where x(t) is state variable vector (superscript “′” indicates anestimating value); u(t) is input vector; A, B is coefficient matrix ofstate equation; y(t) is obsevable sensor output vector and is expressedas:

y(t)=[δ_(s)(dφ/dt)_(s)]^(T)

[0041] The vehicle slip angle β_(s) detected by sensor is obtained byintegrating the vehicle slip angular velocity (dβ/dt)_(s) detected bysensor. The vehicle slip angular velocity (dβ/dt)_(s) is obtained fromthe formula (3) based on the lateral acceleration (d²y/dt²). detected bysensor and the yaw rate (dφ/dt), detected by sensor; C is matrix (inthis embodiment, unit matrix) indicating the relationship between sensoroutput and state variable and K is feed-back gain matrix that can bearbitrarily established and C, K is expressed respectively as follows:$C = \begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix}$ $K = \begin{bmatrix}k_{11} & k_{12} \\k_{21} & k_{22}\end{bmatrix}$

[0042] Hence, the actual yaw angular acceleration (d²φ/dt²)₀ from theobserver and the actual vehicle slip angular velocity (dβ/dt)₀ arecalculated by the following formulas (11) and (12): $\begin{matrix}{( {{^{2}\varphi}/{t^{2}}} )_{0} = {{a_{11} \cdot ( {{\varphi}/{t}} )_{0}} + {a_{12} \cdot \beta_{0}} + {b_{11} \cdot \delta_{fs}} + {k_{11} \cdot ( {( {{\varphi}/{t}} )_{s} - ( {{\varphi}/{t}} )_{0}} )} + {k_{12} \cdot ( {\beta_{s} - \beta_{0}} )}}} & (11) \\{( {{\beta}/{t}} )_{0} = {{a_{21} \cdot ( {{\varphi}/{t}} )_{0}} + {a_{22} \cdot \beta_{0}} + {k_{21} \cdot ( {( {{\varphi}/{t}} )_{s} - ( {{\varphi}/{t}} )_{0}} )} + {k_{22} \cdot ( {\beta_{s} - \beta_{0}} )}}} & (12)\end{matrix}$

[0043] Accordingly, an actual yaw rate (dφ/dt)₀ and an actual vehicleslip angle β₀ are calculated by integrating thus calculated actual yawangular acceleration (d²φ/dt²)₀ and actual vehicle slip angular velocity(dβ/dt)₀. Further, an actual front wheel slip angle β_(f0) is calculatedby substituting the actual vehicle slip angle β₀ and the actual yaw rate(dφ/dt)₀ into the formula (6),respectively.

[0044] In the high friction coefficient road reference value estimatingsection 11 and the actual value estimating section 12, when the vehiclespeed Vs=0, the calculation can not be performed due to the division by0. Hence, when the vehicle travels at extremely low speeds, for examplebelow 10 km/h, the yaw rate and the lateral acceleration are replacedwith sensor values respectively. That is,

(dφ/dt)_(H)=(dφ/dt)_(L)=(dφ/dt)₀=(dφ/dt)_(s)

[0045] Further, the vehicle slip angle can be expressed from thegeometric relationship of the turning on the stationary circle as:

β_(H)=β_(L)=β₀=δ_(fs) ·L _(r)/(L _(f) +L _(r))

[0046] At this time, since no cornering force is generated, the frontwheel slip angle is 0.

β_(fH)=β_(fL)=β_(f0)=0

[0047] The Lissajou figure processing section 13 inputs vehicle speedVs, lateral acceleration (d²y/dt²)_(s), high friction coefficient roadreference yaw rate (dφ/dt)_(H), high friction coefficient road referenceyaw angular acceleration (d²φ/dt²), and actual yaw rate (dφ/dt)₀ andforms a Lissajou's figure based on the high friction coefficient roadreference yaw rate (dφ/dt)_(H) and the actual yaw rate (dφ/dt)₀.Further, the Lissajou figure processing section 13 calculates a gradientr and an area S of of the Lissajou's figure and outputs those to theroad friction coefficient estimating section 14. Further, the Lissajoufigure processing section 13 calculates a steering pattern variable Aφin integrating time T_(s) which will be described hereinafter, furtherdetermines a maximum value (d²y/dt²)_(MAX) of lateral accelerationsensor values (d²y/dt²)_(H) in integrating time T_(s) and outputs thesesteering pattern variable Aφ and maximum value (d²y/dt²)_(MAX) to theroad friction coefficient estimating section 14.

[0048] The integrating time Ts is defined as a time interval duringwhich the high friction coefficient road reference yaw rate (dφ/dt)_(H)has the same sign as the actual yaw rate (dφ/dt)₀ as shown in FIG. 4.Further, the gradient r is defined as a mean value of a ratio r_(i) ofhigh friction coefficient road reference yaw rate (dφ/dt)_(H) to actualyaw rate (dφ/dt)₀ (r_(i)=(dφ/dt)_(H)/(dφ/dt)₀). That is,

r=(1/n)·Σr _(i)   (13)

[0049] where n is a number of data in the integrating time T_(s).

[0050] As shown in FIG. 5, the area S of Lissajou's figure is obtainedby integrating small triangular areas. For example, letting a point(x_(Hn−1), y_(0n−1)) be a value one cycle (Δt=10 milliseconds) before apoint (x_(Hn), y_(0n)), a small triangular area ΔS_(H) is:

ΔS _(H)=(½)·|x _(Hn−1)·(dy _(0n−1) /dt)−y _(0n−1)·(dx _(Hn−1) /dt)|·Δt  (14)

[0051] The steering pattern variable Aφ is a variable for indicating anemergency condition of the steering in integrating time Ts and iscalculated by the following formula (15):

ΔAφ=∫|(d ² φ/dt ²)_(H) |dt (hatched line portion of FIG. 6)

Aφ=ΔAφ ²   (15)

[0052] The reason why ΔAφ is squared is to nonlinearize Aφ.

[0053] The road friction coefficient estimating section 14 inputsgradient r of the Lissajou's figure, area S thereof. Steering patternvariable Aφ and maximum value (d²y/dt²)_(MAX) of lateral acceleration,estimates road friction coefficient and outputs it.

[0054] Specifically, in the road friction coefficient estimating section14, the road friction coefficient is estimated by two methods accordingto the gradient r of a Lissajou's figure.

[0055] First, in case where the gradient of a Lissajou's figure is inthe neighborhood of 45 degrees, for example, 0.8<r<1.2, a variable rA(=S/Aφ) is obtained from the steering pattern variable Aφ and the area Sof the Lissajou's figure. Then, an estimating value μ_(A) of the roadfriction coefficient of this time is calculated by comparing thevariable rA of this time with a threshold value which has beenexperimentally determined beforehand for various road surfaces withdifferent friction coefficients. In this embodiment of the presentinvention, as shown in FIG. 7, for example in case where the vehicletravels on a snowy frozen road and the variable rA is established to avariable rA03 (road friction coefficient=0.3), an estimating value μ_(A)of road friction coefficient this time is:

μ_(A)=−(0.7/rA03)·rA+1.0   (16)

[0056] Further, in case where the gradient of the Lissajou's figure isin a range out of the neighborhood of 45 degrees (for example, r≦0.8 orr≧1.2), the value of lateral acceleration (d²y/dt²)_(MAX) divided bygravitational acceleration is a road friction coefficient estimatingvalue μ_(y).

[0057] Thus obtained road friction coefficient estimating values μ_(A)or μ_(y) is an output value μ_(out) out of the road friction coefficientestimating value. The Lissajou figure processing section 13 and the roadfriction coefficient estimating section 14 constitute a road frictioncoefficient estimating means.

[0058] The yaw rate has a small delay with respect to the steering inputwhen the vehicle travels on a road surface with high frictioncoefficient and has a large delay with respect to the steering inputwhen the vehicle travels on a road surface with low frictioncoefficient. Since it is difficult to calculate the delay in real time,an area S of a Lissajou's figure (the size of the area presents thedelay between two waveforms as shown in FIGS. 8a and 8 b) is obtained.Then, the road friction coefficient is estimated by comparing this areaS with other area.

[0059] However, in case where the Lissajou's figure produces a change inboth delay and size between two waveforms as shown in FIG. 8c, thegradient of the figure changes substantially (largely change from 45degrees) and consequently the area differs from the one accompanied onlyby delay. Hence, when the effect of nonlinearity of tire is strong asshown in FIG. 9a, the Lissajou's figure of this moment changes in itsgradient r and further the area S differs from the one having normaldelay. As a result, it becomes difficult to estimate the road frictioncoefficient by comparing the area with other one.

[0060] Accordingly, first it is of importance to make a judgment from agradient r of Lissajou's figure. That is, in case where the gradient ofa Lissajou's figure is in the neighborhood of 45 degrees, it is judgedthat the tire is in a linear zone and therefore the road frictioncoefficient should be estimated based on an area S of the Lissajou'sfigure. On the other hand, in case where the gradient of a Lissajou'sfigure is in a range out of the neighborhood of 45 degrees, it is judgedthat the tire is in a nonlinear zone and therefore the road frictioncoefficient should be estimated based on a lateral acceleration(d²y/dt²)_(MAX).

[0061] Further, generally the delay of yaw rate also changes accordingto driver's steering condition. That is, yaw rate tends to be delayedmore, as a driver turns the steering wheel fast and tends to be delayedless, as the driver turns the steering wheel slowly. Taking notice ofthe pattern of delay of yaw rate with respect to the steering condition,an accurate estimation of road friction coefficient is available. Hence,in estimating road friction coefficient from the area S of Lissajou'sfigure, the emergency condition of steering is expressed as a steeringpattern variable Aφ obtained by squaring the integral of yaw angularacceleration (d²φ/dt²)_(H) and the variable Aφ is used for estimatingroad friction coefficient.

[0062] Processes of estimating road friction coefficients will bedescribed by reference to a flowchart of FIG. 10. This program isexecuted at a specified time interval (for example 10 milliseconds).

[0063] At a step (hereinafter referred to as S) 101, necessaryparameters (sensor values) are read and the program goes to S102.

[0064] At S102, it is judged whether or not vehicle speed V_(s) islarger than the lowest speed value where the vehicle motion model of thehigh friction coefficient reference value estimating section 11 and theactual value estimating section 12 can be applied, for example 10 km/h.As a result of this judgment, in case where the vehicle speed V_(s) islarger than 10 km/h, the program goes to S103 where the high frictioncoefficient road reference yaw rate (dφ/dt)_(H) and the yaw angularacceleration (d²φ/dt²)_(H) are calculated in the high frictioncoefficient reference value estimating section 11 and the actual yawrate (dφ/dt)₀ is also calculated by the observer in the actual valueestimating section 12. Further, as a result of the judgment at S102, incase where the vehicle speed V_(s) is smaller than 10 km/h, the programleaves the routine.

[0065] Then, the program goes to S104 wherein it is judged whether ornot the high friction coefficient road reference yaw rate (dφ/dt)_(H)and the actual yaw rate (dφ/dt)₀ have the same sign and those are withinthe integrating time T_(s).

[0066] As a result of this judgment, in case where it is judged that thehigh friction coefficient road reference yaw rate (dφ/dt)_(H) and theactual yaw rate (dφ/dt)₀ have an identical sign and are within theintegrating time T_(s), the program goes to S105 where it is judgedwhether or not the high friction coefficient road reference yaw rate(dφ/dt)_(H) and the actual yaw rate (dφ/dt)₀ are larger than a specifiedvalue, that is, whether or not the high friction coefficient roadreference yaw rate (dφ/dt)_(H) and the actual yaw rate (dφ/dt)₀ are in arange containing small errors.

[0067] As a result, in case where the high friction coefficient roadreference yaw rate (dφ/dt)_(H) and the actual yaw rate (dφ/dt)₀ arelarger than the specified value, the program goes to S106 where aLissajou figure processing flag F_(lg) is set (F_(lg)=1).

[0068] Next, the program goes to S107 where a ratio r_(i) of the actualyaw rate (dφ/dt)₀ to the high friction coefficient road reference yawrate (dφ/dt)_(H) (=(dφ/dt)₀/(dφ/dt)_(H)) is calculated and goes to S108where a gradient r of Lissajou's figure is calculated based on the r_(i)(accumulated since the integrating time starts) according to the formula(13).

[0069] After that, the program goes to S109 where a small triangulararea ΔS_(H) of Lissajou's figure is calculated and then at S110, thisarea ΔS_(H) is added to the area S of Lissajou's figure which has beenever (since the integrating time starts) accumulated (S=S+ΔS_(H)).

[0070] Then, the program goes to S111 where a maximum value(d²y/dt²)_(MAX) of the inputted lateral acceleration sensor value(d²y/dt²)_(s) is calculated and the program leaves the routine.

[0071] On the other hand, at S104, in case where the high frictioncoefficient road reference yaw rate (dφ/dt)_(H) and the actual yaw rate(dφ/dt)₀ have an identical sign and are out of the integrating timeT_(s), or at S105, in case where either of the high friction coefficientroad reference yaw rate (dφ/dt)_(H) and the actual yaw rate (dφ/dt)₀ issmaller than a specified value and those are within a range ofcontaining errors, the program goes to S112.

[0072] At S112, it is judged whether or not the Lissajou figureprocessing flag Flg is set, that is, whether or not the process hasfinished within the integrating time T_(s). If the Lissajou figureprocessing flag Flg has been set and the process has finished withinT_(s), the program goes to S113. On the other hand, If the Lissajoufigure processing flag Flg has not been set and the process has not yetfinished within T₃, the program leaves the routine.

[0073] At S113, the gradient r of the Lissajou's figure is referred toand in case where the gradient r is in the neighborhood of 45 degrees,that is, in case of 0.8<r<1.2, it is judged that the tire is in a linearzone and the program goes to S114 where the steering pattern variable Aφis calculated based on the high friction coefficient road reference yawangular acceleration (d²φ/dt²)_(H) according to the formula (15) and theroad friction coefficient estimating value μ_(A) is calculated based onthis steering pattern variable Aφ and the area S of the Lissajou'sfigure according to the formula (16).

[0074] After that, the program goes to S115 where this road frictioncoefficient estimating value μ_(A) is established to a road frictioncoefficient estimating output value μ_(out) to be outputted from thecontrol section 2 and goes to S116 where the Lissajou figure processingflag F_(lg) is cleared (F_(lg)=0). Then, at S117, the gradient r andarea S of the Lissajou's figure and the lateral acceleration maximumvalue (d²y/dt²)_(MAX) that are stored for estimating a road frictioncoefficient this time, are cleared and the program leaves the routine.

[0075] On the other hand, as a result of the judgment of the gradient rof the Lissajou's figure at S113, in case where the gradient is awayfrom the neighborhood of 45 degrees, that is, in case of r≦0.8 or r≧1.2,it is judged that the tire is in a nonlinear zone and the program goesto S118 in which a road friction coefficient estimating value μ_(y) isobtained by dividing the lateral acceleration maximum value(d²y/dt²)_(MAX) by gravitational acceleration.

[0076] Then, the program goes to S119 where this road frictioncoefficient estimating value μ_(y) is established to a road frictioncoefficient estimating output value μ_(out) to be outputted from thecontrol section 2 and goes to S116 where the Lissajou figure processingflag F_(lg) is cleared (F_(lg)=0). Then, at S117, the gradient r andarea S of the Lissajou's figure and the lateral acceleration maximumvalue (d²y/dt²)_(MAX) that are stored for estimating a road frictioncoefficient this time, are cleared and the program leaves the routine.

[0077] Thus, according to the embodiment of the present invention, sincea road friction coefficient can be estimated only by the outputs fromthe high friction coefficient road reference value estimating section 11and the actual value estimating section 12, the road frictioncoefficients estimating apparatus has an advantage of that theconstruction of the apparatus is simple and the amount of calculation issmall. Further, since in a linear zone of tire the road frictioncoefficient is estimated based on the change of the area S of Lissajou'sfigure and in a nonlinear zone of tire the road friction coefficient isestimated based on the lateral acceleration maximum value(d²y/dt²)_(MAX), road friction coefficients can be estimated stably andaccurately over a wide range of traveling condition. Further, sinceconsidering the degree of emergency of a vehicle driver the area S ofLissajou's figure is corrected by the steering pattern variable Aφ, amore accurate estimation of road friction coefficients can be performed.

[0078] While the presently preferred embodiment of the present inventionhas been shown and described, it is to be understood that thisdisclosure is for the purpose of illustration and that various changesand modifications may be made without departing from the scope of theinvention as set forth in the appended claims.

What is claimed is:
 1. A road friction coefficient estimating apparatusfor a vehicle comprising: an actual value estimating means forestimating an actual value of a vehicle motion parameter; a highfriction coefficient road reference value estimating means forestimating a high friction coefficient road reference value of saidvehicle motion parameter based on a vehicle motion model when saidvehicle travels on a road surface with high friction coefficient; and aroad friction coefficient estimating means for forming a Lissajou'sfigure based on said actual value and said high friction coefficientroad reference value and for estimating a road friction coefficientaccording to a gradient and an area of said Lissajou's figure.
 2. Theroad friction coefficient estimating apparatus according to claim 1,wherein said road friction coefficient estimating means estimates saidroad friction coefficient based on said area of said Lissajou's figurewhen said gradient of said Lissajou's figure is in the neighborhood of45 degrees.
 3. The road friction coefficient estimating apparatusaccording to claim 2, wherein said area of said Lissajou's figure iscorrected according to a degree of emergency of steering.
 4. The roadfriction coefficient estimating apparatus according to claim 1, whereinsaid road friction coefficient estimating means estimates said roadfriction coefficient based on a lateral acceleration of said vehiclewhen said gradient of said Lissajou's figure is in a range out of theneighborhood of 45 degrees.